All the possible values of k will have a pair of one negative and one positive integer except for -24 and -25. So when u add all of them -24 and -25 will remain as they don't have a corresponding positive Hence, -49


U can also list down all numbers
Numbers betn 0 and -26
-(1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 21 23 24 25)
Numbers betn 0 and 24
(1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23)

-24 and -25 remain as it is. Hence D

This is time to not panic and be methodical - the GMAT will not ask you to do such a crazy sum. questions about inequalities that span zero are often about the relationship with zero. start thinking how the numbers relate.

the first negative integer will be -25,-24, -23, -22 (ok so we see how that is going to go)

Now look at the positive integers the first will be 23, then 22, 21 .... and hopefully you will notice the pattern that 23-23= 0 and that will happen as you move toward zero. only -25 and -24 are left without positive partners so if you add them you get - 49.

Also, it's not that crazy of a sum to add up if you wanted to:

Number of terms:
25 negatives, 1 zero, 23 positives = 49

Average of terms: (-25 + 23)/2 = -2/2 = -1

Sum = Number of terms * Average = 49 * -1 = -49

IMO:D